Cooperative advertising in a capacitated manufacturer–retailer supply chain: a game‐theoretic approach

Abstract To achieve a more realistic understanding of how the supply chain's components interact, it is helpful to consider the operational limitations of the underlying supply chain while analyzing cooperative advertising. This paper studies cooperative advertising in a manufacturer–retailer supply chain under the practical operational assumption that the manufacturer's production capacity is limited. The retailer advertises locally, and the manufacturer advertises in national media and supports part of the retailer's promotional costs. Equilibria are determined under two different scenarios. In the first scenario, both retailer and manufacturer move simultaneously, while in the second scenario, they move sequentially, with the manufacturer being the leader. The sales function is a bivariate version of the diminishing returns response function. When the production capacity is unlimited, several important properties can be proven, which cannot be shown analytically for the existing sales functions. Considering the production‐capacity constraint leads to new managerial insights into cooperative advertising. For example, only if the production capacity is large enough, both manufacturer and retailer are better off under the second scenario than the first scenario. In other words, the sequential move is not necessarily Pareto‐improving when the production capacity is limited. It is also observed that, under the first scenario, there are multiple equilibria whenever the production capacity is not too high. Under the second scenario, the manufacturer supports the retailer only when the retailer's margin is relatively small compared to the manufacturer's margin and production capacity.